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Equilateral Hyperbolas and Triangles in the Hyperbolic Plane

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Geometry of Minkowski Space-Time

Part of the book series: SpringerBriefs in Physics ((SpringerBriefs in Physics))

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Abstract

The equilateral hyperbolas, represented in the Minkowski space-time, hold the same properties of circles in Euclidean plane and satisfy similar theorems. At the same time equivalent relations to the ones in Euclidean plane between circles and triangles are obtained in hyperbolic plane between equilateral hyperbolas and triangles.

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References

  1. I.M. Yaglom, A Simple Non-euclidean Geometry and its Physical Basis. (Springer-Verlag, New York, 1979)

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  2. F. Catoni, R. Cannata, V. Catoni, P. Zampetti, Two-dimensional hypercomplex numbers and related trigonometries and geometries. Adv. Appl. Clifford Al. 14(1), 47 (2004)

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  3. F. Catoni, D. Boccaletti, R. Cannata, V. Catoni, E. Nichelatti, P. Zampetti, The Mathematics of Minkowski Space-Time. (Birkhäuser Verlag, Basel, 2008)

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Authors and Affiliations

  1. ENEA, Via Veglia 10, 00141, Rome, Italy

    Francesco Catoni & Vincenzo Catoni

  2. Department of Mathematics, University of Rome “La Sapienza”, Piazzale Aldo Moro 2, 00185, Rome, Italy

    Dino Boccaletti

  3. Casaccia Research Centre, ENEA, Via Anguillarese 301, 00123, Rome, Italy

    Roberto Cannata & Paolo Zampetti

Authors
  1. Francesco Catoni
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  2. Dino Boccaletti
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  3. Roberto Cannata
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  4. Vincenzo Catoni
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  5. Paolo Zampetti
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Corresponding author

Correspondence to Francesco Catoni .

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© 2011 Francesco Catoni

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Catoni, F., Boccaletti, D., Cannata, R., Catoni, V., Zampetti, P. (2011). Equilateral Hyperbolas and Triangles in the Hyperbolic Plane. In: Geometry of Minkowski Space-Time. SpringerBriefs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17977-8_5

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  • DOI: https://doi.org/10.1007/978-3-642-17977-8_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17976-1

  • Online ISBN: 978-3-642-17977-8

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

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